Dr David Walker has been speaking after St Chrysotom's put on a performance of 'The Gospel According to Jesus, Queen of Heaven'.
The Bishop had asked for the play not to be held in a church but has been criticised by some for not blocking the performance.
According to its producers, the play was a "unique and extraordinary" performance which "combines theatre with storytelling, spoken word and ritual, in the beautiful setting of a Manchester church."
The performance, a one-woman show, featured Jo Clifford, an award-winning playwright, returning to the world as Jesus and retelling Bible stories.
She said it was not meant to be sacrilegious.
In a statement, responding to the play, Bishop David said: "That an artistic performance is offensive to Christians does not of itself amount to grounds for seeking to prevent it taking place. In a richly diverse society, of which Manchester is a proud standard bearer, none of us has the right to be protected from being offended. It is only when offence reaches the level of incitement to hatred that the law properly comes into play.
"However, there are particular sensitivities surrounding theatrical performances in churches beyond what might properly apply to any other venue. The process for approving a performance in a church, together with the criteria that should inform the decision, are set out in canon F16, which is part of the laws of the Church of England. The responsibility clearly lies solely with the local minister, unless he or she elects to refer it to the bishop for determination.
"That I cannot support this particular performance, and have urged that consideration be given to transferring it to a less contentious venue, in no way weakens the support I and my colleagues continue to give to the transgendered members of our community and our churches, not least during the annual Sparkle weekend in the city centre."
During the play Jo Clifford, a trans-female, says "I love my Mum. I am the daughter of God and almost certainty the son also."
Former Bishop of Rochester, Rt Revd Michael Nazir-Ali, said in The Mail on Sunday: "It is quite clear from the Gospels that the identity of Jesus is male, his 'mum' is Mary and he always refers to God as 'Father', so to suggest otherwise is contrary to Christian teaching."
